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This vanguard work addresses both the stabilization and optimization of networked control systems, which have inherent stochasticity caused by communication constraints.

Research for this book began when Yüksel was an ECE graduate student, working with Professor Başar in the Coordinated Science Laboratory.

Networked control systems operate like teams. Take smart grids for example: those responsive, automated power networks that are on the ever-nearing technological horizon. The sensors that determine power consumption at individual houses or production at single wind turbines are like the reconnaissance team members in a game of capture the flag, the spies crawling under bushes at the frontline. Both collect information and send it back to a central decision-maker (the spies via walkie-talkies, the grid with optical fiber), and the decision-maker determines a suitable action. If the flag is unguarded, the fleet-footed offense is directed to run for it. If more energy consumption is reported, an additional turbine is engaged.

Tamer Basar

The problem with networked systems, however, is communication. Since the members are separated over some distance, physical characteristics of the communication lines may limit information transfer. Perhaps the optical fibers have bandwidth constraints, and with the walkie-talkies, the spies must take turns calling into the base camp and the reception is staticky at best. “That is where stochasticity comes in,” said Professor Tamer Basar. “You cannot send data at the rate that you want to send it because there are all kinds of physical restrictions.”

“[This is] one of the first, if not the first, book which covers both optimization as well stabilization of systems which are networked,” Başar said. “I think the interesting or exciting part of this is that this is one of the few frameworks where applications could be all the way from engineering to economics, from hard sciences to soft sciences.” In other words, the mathematical theories presented in the book have applications beyond networked control systems, in any team-like situations with limited communication.

In these systems, satisfactory performance and stability require at least a minimum amount of information transfer. Suitable smart grid operation, for instance, necessitates power consumption data, sent from electricity meters at houses and businesses, as well as the corresponding power production data for wind turbines and other power generators. If that basic information isn’t reliably shared over the network, the two factors fall out of balance, and the system will fail to achieve optimal performance. Five chapters of Başar and Yüksel’s book present mathematical theories for mitigating instability, including substantial discussion of state-dependent, random-time variables (better known as “drift criteria”). The presentation is comprehensive and mathematically rigorous.

Such networked structures also tend to be decentralized, with multiple decision-makers that have differing access to information. In a decentralized game of capture the flag, each team member might decide to run for the flag at any given moment. (There is no single team captain saying, “Runner, go for the flag now.”) But without some coordination between the team members (regarding the known locations of the opposing team, for example), the repercussions could bode poorly.

Stochastic Networked Control Systems (Birkhäuser)

Başar and Yüksel present optimization strategies for these decentralized networks. “The question is whether individual decision-makers can develop reliable beliefs on what the others are thinking, or what their capabilities are, and whether eventually, in a dynamic environment, these beliefs converge,” Başar said. “We call it belief propagation.”

Among numerous applications, belief propagation is useful for automated aircrafts, especially in military settings where there must be coordination between the aircrafts and ground forces. During combat, some information may be intentionally withheld from certain decision-makers depending on the security classification. For these situations, Başar and Yüksel offer formulas that facilitate decision-making based on shared beliefs. There are also parallels in economics, where companies might establish mutually agreeable production levels without sharing any managerial or financial information.

Throughout the book, Başar and Yüksel endeavor to introduce a conceptual framework for approaching and mitigating performance limitations in these systems. They elucidate issues that system designers should account for, and tradeoffs that are faced when implementing efficient solutions. “Software development is also part of it. We don’t discuss that, but that would be one of the applications of this,” Başar said. “One has to develop algorithms, and one has to take into account that…the algorithms have to be efficient and have to be real-time implementable.”

The book is an outgrowth of research that Yüksel began as an ECE graduate student, working in the Coordinated Science Laboratory, where Başar is a professor. Yüksel is now an associate professor of mathematics and engineering at Queen’s University at Kingston, Ontario. Başar holds the Swanlund Endowed Chair at Illinois and is also a professor at the Center for Advanced Study and the Information Trust Institute. “It’s good to continue collaboration with one’s former students and to see something like this come out,” Başar said. “We think it is a very solid contribution to the literature in this field.”